def test_project_clone(self):
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
graph = create_graph_from_text(g_str)
# Test clone
cloned = gtn.clone(graph)
self.assertTrue(gtn.equal(graph, cloned))
# Test projecting input
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
inputExpected = create_graph_from_text(g_str)
self.assertTrue(gtn.equal(gtn.project_input(graph), inputExpected))
# Test projecting output
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
outputExpected = create_graph_from_text(g_str)
self.assertTrue(gtn.equal(gtn.project_output(graph), outputExpected))
def test_viterbi_path_grad(self):
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 3",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
g = create_graph_from_text(g_str)
gtn.backward(gtn.viterbi_path(g))
expected = [1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0]
self.assertEqual(g.grad().weights_to_list(), expected)
g.zero_grad()
def forward_fn(g):
paths = [
gtn.viterbi_path(g),
gtn.viterbi_path(g),
gtn.viterbi_path(g)
]
return gtn.forward_score(gtn.union(paths))
gtn.backward(forward_fn(g))
self.assertTrue(numerical_grad_check(forward_fn, g, 1e-3, 1e-5))
def test_viterbi_score_grad(self):
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 1)
g.add_arc(0, 1, 1, 1, 2)
g.add_arc(0, 1, 2, 2, 3)
g.add_arc(1, 2, 0, 0, 1)
g.add_arc(1, 2, 1, 1, 2)
g.add_arc(1, 2, 2, 2, 3)
gtn.backward(gtn.viterbi_score(g))
expected = [0.0, 0.0, 1.0, 0.0, 0.0, 1.0]
self.assertEqual(g.grad().weights_to_list(), expected)
# Handle two start nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, -5)
g.add_arc(0, 2, 0, 0, 1)
g.add_arc(1, 2, 0, 0, 2)
gtn.backward(gtn.viterbi_score(g))
expected = [0.0, 0.0, 1.0]
self.assertEqual(g.grad().weights_to_list(), expected)
# Handle two accept nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 2)
g.add_arc(0, 2, 0, 0, 2)
g.add_arc(1, 2, 0, 0, 2)
gtn.backward(gtn.viterbi_score(g))
expected = [1.0, 0.0, 1.0]
self.assertEqual(g.grad().weights_to_list(), expected)
# A more complex test case
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
g = create_graph_from_text(g_str)
gtn.backward(gtn.viterbi_score(g))
# two possible paths with same viterbi score
expected1 = [1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0]
expected2 = [1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0]
self.assertTrue(g.grad().weights_to_list() == expected1
or g.grad().weights_to_list() == expected2)
def test_viterbi_score(self):
# Check score of empty graph
g = gtn.Graph()
self.assertEqual(gtn.viterbi_score(g).item(), -math.inf)
# A simple test case
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 1)
g.add_arc(0, 1, 1, 1, 2)
g.add_arc(0, 1, 2, 2, 3)
g.add_arc(1, 2, 0, 0, 1)
g.add_arc(1, 2, 1, 1, 2)
g.add_arc(1, 2, 2, 2, 3)
self.assertEqual(gtn.viterbi_score(g).item(), 6.0)
# Handle two start nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, -5)
g.add_arc(0, 2, 0, 0, 1)
g.add_arc(1, 2, 0, 0, 2)
self.assertEqual(gtn.viterbi_score(g).item(), 2.0)
# Handle two accept nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 2)
g.add_arc(0, 2, 0, 0, 2)
g.add_arc(1, 2, 0, 0, 2)
self.assertEqual(gtn.viterbi_score(g).item(), 4.0)
# A more complex test case
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
g = create_graph_from_text(g_str)
self.assertEqual(gtn.viterbi_score(g).item(), 7.0)
def test_savetxt(self):
# Acceptor test
g = gtn.Graph()
g.add_node(True)
g.add_node(True)
g.add_node()
g.add_node()
g.add_node(False, True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 1.1)
g.add_arc(1, 2, 1, 1, 2.1)
g.add_arc(2, 3, 2, 2, 3.1)
g.add_arc(3, 4, 3, 3, 4.1)
g.add_arc(4, 5, 4, 4, 5.1)
g_str = [
"0 1",
"4 5",
"0 1 0 0 1.1",
"1 2 1 1 2.1",
"2 3 2 2 3.1",
"3 4 3 3 4.1",
"4 5 4 4 5.1",
]
g = create_graph_from_text(g_str)
_, tmpfile = tempfile.mkstemp()
gtn.savetxt(tmpfile, g)
with open(tmpfile) as f:
lines = f.readlines()
self.assertEqual(len(g_str), len(lines))
for i, line in enumerate(lines):
self.assertEqual(line.strip(), g_str[i])
# Transducer test
g = gtn.Graph()
g.add_node(True)
g.add_node(True)
g.add_node()
g.add_node()
g.add_node(False, True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 1, 1.1)
g.add_arc(1, 2, 1, 2, 2.1)
g.add_arc(2, 3, 2, 3, 3.1)
g.add_arc(3, 4, 3, 4, 4.1)
g.add_arc(4, 5, 4, gtn.epsilon, 5.1)
g_str = [
"0 1",
"4 5",
"0 1 0 1 1.1",
"1 2 1 2 2.1",
"2 3 2 3 3.1",
"3 4 3 4 4.1",
"4 5 4 -1 5.1",
]
g = create_graph_from_text(g_str)
_, tmpfile = tempfile.mkstemp()
gtn.savetxt(tmpfile, g)
with open(tmpfile) as f:
lines = f.readlines()
self.assertEqual(len(g_str), len(lines))
for i, line in enumerate(lines):
self.assertEqual(line.strip(), g_str[i])
def test_loadtxt(self):
g1 = gtn.Graph()
g1.add_node(True, True)
g1.add_node(False, True)
g1.add_node()
g1.add_arc(0, 0, 1)
g1.add_arc(0, 2, 1, 1, 1.1)
g1.add_arc(2, 1, 2, 2, 2.1)
g_str = ["0", "0 1", "0 0 1 1 0", "0 2 1 1 1.1", "2 1 2 2 2.1"]
g2 = create_graph_from_text(g_str)
self.assertTrue(gtn.equal(g1, g2))
self.assertTrue(gtn.isomorphic(g1, g2))
_, tmpfile = tempfile.mkstemp()
# Write the test file
gtn.savetxt(tmpfile, g2)
g3 = gtn.loadtxt(tmpfile)
self.assertTrue(gtn.equal(g1, g3))
# Empty graph doesn't load
g_str = [""]
self.assertRaises(ValueError, create_graph_from_text, g_str)
# Graph without accept nodes doesn't load
g_str = ["1"]
self.assertRaises(ValueError, create_graph_from_text, g_str)
# Graph with repeat start nodes doesn't load
g_str = ["1 0 0", "0 1"]
self.assertRaises(ValueError, create_graph_from_text, g_str)
# Graph loads if the start and accept nodes are specified
g_str = ["0", "1"]
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
self.assertTrue(gtn.equal(g, create_graph_from_text(g_str)))
# Graph doesn't load if arc incorrect
g_str = ["0", "1", "0 2"]
self.assertRaises(ValueError, create_graph_from_text, g_str)
g_str = ["0", "1", "0 1 2 3 4 5"]
self.assertRaises(ValueError, create_graph_from_text, g_str)
# Transducer loads
g1 = gtn.Graph()
g1.add_node(True, True)
g1.add_node(False, True)
g1.add_node()
g1.add_arc(0, 0, 1, 1)
g1.add_arc(0, 2, 1, 2, 1.1)
g1.add_arc(2, 1, 2, 3, 2.1)
g_str = ["0", "0 1", "0 0 1", "0 2 1 2 1.1", "2 1 2 3 2.1"]
g2 = create_graph_from_text(g_str)
self.assertTrue(gtn.equal(g1, g2))
self.assertTrue(gtn.isomorphic(g1, g2))
def test_forward_score_grad(self):
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 1)
g.add_arc(0, 1, 1, 1, 2)
g.add_arc(0, 1, 2, 2, 3)
g.add_arc(1, 2, 0, 0, 1)
g.add_arc(1, 2, 1, 1, 2)
g.add_arc(1, 2, 2, 2, 3)
gtn.backward(gtn.forward_score(g))
self.assertTrue(numerical_grad_check(gtn.forward_score, g, 1e-3, 1e-3))
# Handle two start nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, -5)
g.add_arc(0, 2, 0, 0, 1)
g.add_arc(1, 2, 0, 0, 2)
gtn.backward(gtn.forward_score(g))
self.assertTrue(numerical_grad_check(gtn.forward_score, g, 1e-3, 1e-3))
denom = 1 / (math.exp(-3) + math.exp(1) + math.exp(2))
grad = g.grad()
grad_weights = grad.weights_to_list()
self.assertAlmostEqual(grad_weights[0], (denom * math.exp(-3)))
self.assertAlmostEqual(grad_weights[1], (denom * math.exp(1)))
self.assertAlmostEqual(grad_weights[2],
(denom * (math.exp(-3) + math.exp(2))))
# Handle two accept nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 2)
g.add_arc(0, 2, 0, 0, 2)
g.add_arc(1, 2, 0, 0, 2)
gtn.backward(gtn.forward_score(g))
self.assertTrue(numerical_grad_check(gtn.forward_score, g, 1e-3, 1e-3))
denom = 1 / (2 * math.exp(2) + math.exp(4))
grad = g.grad()
grad_weights = grad.weights_to_list()
self.assertAlmostEqual(grad_weights[0],
(denom * (math.exp(2) + math.exp(4))),
places=5)
self.assertAlmostEqual(grad_weights[1], (denom * math.exp(2)),
places=5)
self.assertAlmostEqual(grad_weights[2], (denom * math.exp(4)),
places=5)
# Handle case where some arcs don't lead to accepting states
g = gtn.Graph()
g.add_node(True)
g.add_node(False, False)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 2)
g.add_arc(0, 2, 0, 0, 2)
gtn.backward(gtn.forward_score(g))
self.assertTrue(numerical_grad_check(gtn.forward_score, g, 1e-3, 1e-3))
grad = g.grad()
grad_weights = grad.weights_to_list()
self.assertAlmostEqual(grad_weights[0], (0.0))
self.assertAlmostEqual(grad_weights[1], (1.0))
# Handles negative infinity
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, -math.inf)
g.add_arc(0, 1, 1, 1, -math.inf)
gtn.backward(gtn.forward_score(g))
grad = g.grad()
grad_weights = grad.weights_to_list()
self.assertTrue(math.isnan(grad_weights[0]))
self.assertTrue(math.isnan(grad_weights[1]))
g2 = gtn.Graph()
g2.add_node(True)
g2.add_node(False, True)
g2.add_arc(0, 1, 0, 0, -math.inf)
g2.add_arc(0, 1, 1, 1, 1.0)
gtn.backward(gtn.forward_score(g2))
grad2 = g2.grad()
grad_weights = grad2.weights_to_list()
self.assertAlmostEqual(grad_weights[0], (0.0))
self.assertAlmostEqual(grad_weights[1], (1.0))
# Handles infinity
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, math.inf)
g.add_arc(0, 1, 1, 1, math.inf)
gtn.backward(gtn.forward_score(g))
grad = g.grad()
grad_weights = grad.weights_to_list()
self.assertTrue(math.isnan(grad_weights[0]))
self.assertTrue(math.isnan(grad_weights[1]))
g2 = gtn.Graph()
g2.add_node(True)
g2.add_node(False, True)
g2.add_arc(0, 1, 0, 0, math.inf)
g2.add_arc(0, 1, 1, 1, 1.0)
gtn.backward(gtn.forward_score(g2))
grad2 = g2.grad()
grad_weights = grad.weights_to_list()
self.assertTrue(math.isnan(grad_weights[0]))
self.assertTrue(math.isnan(grad_weights[1]))
# A more complex test case
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
g = create_graph_from_text(g_str)
gtn.backward(gtn.forward_score(g))
self.assertTrue(numerical_grad_check(gtn.forward_score, g, 1e-3, 1e-3))
def test_composition(self):
# Compos,ing with an empty graph gives an empty graph
g1 = gtn.Graph()
g2 = gtn.Graph()
self.assertTrue(gtn.equal(gtn.compose(g1, g2), gtn.Graph()))
g1.add_node(True)
g1.add_node()
g1.add_arc(0, 1, 0)
g2.add_node(True)
g2.add_node(False, True)
g2.add_arc(0, 1, 0)
g2.add_arc(0, 1, 0)
self.assertTrue(gtn.equal(gtn.compose(g1, g2), gtn.Graph()))
self.assertTrue(gtn.equal(gtn.compose(g2, g1), gtn.Graph()))
self.assertTrue(gtn.equal(gtn.intersect(g2, g1), gtn.Graph()))
# Check singly sorted version
g1.arc_sort(True)
self.assertTrue(gtn.equal(gtn.compose(g1, g2), gtn.Graph()))
# Check doubly sorted version
g2.arc_sort()
self.assertTrue(gtn.equal(gtn.compose(g1, g2), gtn.Graph()))
# Self-loop in the composed graph
g1 = gtn.Graph()
g1.add_node(True)
g1.add_node(False, True)
g1.add_arc(0, 0, 0)
g1.add_arc(0, 1, 1)
g1.add_arc(1, 1, 2)
g2 = gtn.Graph()
g2.add_node(True)
g2.add_node()
g2.add_node(False, True)
g2.add_arc(0, 1, 0)
g2.add_arc(1, 1, 0)
g2.add_arc(1, 2, 1)
g_str = ["0", "2", "0 1 0", "1 1 0", "1 2 1"]
expected = create_graph_from_text(g_str)
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
self.assertTrue(gtn.isomorphic(gtn.intersect(g1, g2), expected))
# Check singly sorted version
g1.arc_sort(True)
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
# Check doubly sorted version
g2.arc_sort()
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
# Loop in the composed graph
g1 = gtn.Graph()
g1.add_node(True)
g1.add_node(False, True)
g1.add_arc(0, 1, 0)
g1.add_arc(1, 1, 1)
g1.add_arc(1, 0, 0)
g2 = gtn.Graph()
g2.add_node(True)
g2.add_node(False, True)
g2.add_arc(0, 0, 0)
g2.add_arc(0, 1, 1)
g2.add_arc(1, 0, 1)
g_str = ["0", "2", "0 1 0", "1 0 0", "1 2 1", "2 1 1"]
expected = create_graph_from_text(g_str)
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
self.assertTrue(gtn.isomorphic(gtn.intersect(g1, g2), expected))
# Check singly sorted version
g1.arc_sort(True)
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
# Check doubly sorted version
g2.arc_sort()
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
g1 = gtn.Graph()
g1.add_node(True)
g1.add_node()
g1.add_node()
g1.add_node()
g1.add_node(False, True)
for i in range(g1.num_nodes() - 1):
for j in range(3):
g1.add_arc(i, i + 1, j, j, j)
g2 = gtn.Graph()
g2.add_node(True)
g2.add_node()
g2.add_node(False, True)
g2.add_arc(0, 1, 0, 0, 3.5)
g2.add_arc(1, 1, 0, 0, 2.5)
g2.add_arc(1, 2, 1, 1, 1.5)
g2.add_arc(2, 2, 1, 1, 4.5)
g_str = [
"0",
"6",
"0 1 0 0 3.5",
"1 2 0 0 2.5",
"1 4 1 1 2.5",
"2 3 0 0 2.5",
"2 5 1 1 2.5",
"4 5 1 1 5.5",
"3 6 1 1 2.5",
"5 6 1 1 5.5",
]
expected = create_graph_from_text(g_str)
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
self.assertTrue(gtn.isomorphic(gtn.intersect(g1, g2), expected))
# Check singly sorted version
g1.arc_sort(True)
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
# Check doubly sorted version
g2.arc_sort()
self.assertTrue(gtn.isomorphic(gtn.compose(g1, g2), expected))
def test_viterbi_path(self):
g = gtn.Graph()
# Empty graph gives empty path
self.assertTrue(gtn.equal(gtn.viterbi_path(g), g))
# Accepting empty string
g.add_node(True, True)
self.assertTrue(gtn.equal(gtn.viterbi_path(g), g))
# A simple test case
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 1)
g.add_arc(0, 1, 1, 1, 2)
g.add_arc(0, 1, 2, 2, 3)
g.add_arc(1, 2, 0, 0, 1)
g.add_arc(1, 2, 1, 1, 2)
g.add_arc(1, 2, 2, 2, 3)
best = gtn.Graph()
best.add_node(True)
best.add_node()
best.add_node(False, True)
best.add_arc(0, 1, 2, 2, 3)
best.add_arc(1, 2, 2, 2, 3)
path = gtn.viterbi_path(g)
self.assertTrue(gtn.rand_equivalent(path, best))
self.assertEqual(gtn.viterbi_score(path).item(), gtn.viterbi_score(g).item())
# Handle a single node.
g = gtn.Graph()
g.add_node(True, True)
best = gtn.Graph()
best.add_node(True, True)
path = gtn.viterbi_path(g)
self.assertTrue(gtn.rand_equivalent(path, best))
self.assertEqual(gtn.viterbi_score(path).item(), gtn.viterbi_score(g).item())
# Handle two start nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, -5)
g.add_arc(0, 2, 0, 0, 1)
g.add_arc(1, 2, 0, 0, 2)
best = gtn.Graph()
best.add_node(True)
best.add_node(False, True)
best.add_arc(0, 1, 0, 0, 2)
path = gtn.viterbi_path(g)
self.assertTrue(gtn.rand_equivalent(path, best))
self.assertEqual(gtn.viterbi_score(path).item(), gtn.viterbi_score(g).item())
# Handle two accept nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 3)
g.add_arc(0, 2, 0, 0, 2)
g.add_arc(1, 2, 0, 0, 2)
best = gtn.Graph()
best.add_node(True)
best.add_node()
best.add_node(False, True)
best.add_arc(0, 1, 0, 0, 3)
best.add_arc(1, 2, 0, 0, 2)
path = gtn.viterbi_path(g)
self.assertTrue(gtn.rand_equivalent(path, best))
self.assertEqual(gtn.viterbi_score(path).item(), gtn.viterbi_score(g).item())
# A more complex test case
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
g = create_graph_from_text(g_str)
# There are three options for the best path, the
# viterbiPath may return any of them.
best1 = gtn.Graph()
best1.add_node(True)
best1.add_node()
best1.add_node()
best1.add_node()
best1.add_node(False, True)
best1.add_arc(0, 1, 0, 0, 2)
best1.add_arc(1, 2, 0, 0, 2)
best1.add_arc(2, 3, 0, 0, 1)
best1.add_arc(3, 4, 0, 0, 2)
best2 = gtn.Graph()
best2.add_node(True)
best2.add_node()
best2.add_node()
best2.add_node()
best2.add_node(False, True)
best2.add_arc(0, 1, 0, 0, 2)
best2.add_arc(1, 2, 0, 0, 2)
best2.add_arc(2, 3, 1, 1, 1)
best2.add_arc(3, 4, 0, 0, 2)
best3 = gtn.Graph()
best3.add_node(True)
best3.add_node()
best3.add_node()
best3.add_node(False, True)
best3.add_arc(0, 1, 0, 0, 2)
best3.add_arc(1, 2, 0, 0, 2)
best3.add_arc(2, 3, 1, 1, 3)
path = gtn.viterbi_path(g)
self.assertTrue(
(
gtn.rand_equivalent(path, best1)
or gtn.rand_equivalent(path, best2)
or gtn.rand_equivalent(path, best3)
)
)
self.assertEqual(gtn.viterbi_score(path).item(), gtn.viterbi_score(g).item())
def test_forward(self):
# Check score of empty graph
g = gtn.Graph()
self.assertEqual(gtn.forward_score(g).item(), -math.inf)
# Throws on self-loops
g = gtn.Graph()
g.add_node(True, True)
g.add_arc(0, 0, 1)
self.assertRaises(ValueError, gtn.forward_score, g)
# Throws on internal self-loop
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0)
g.add_arc(1, 2, 0)
g.add_arc(1, 1, 0)
self.assertRaises(ValueError, gtn.forward_score, g)
# Throws on self-loop in accept node
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0)
g.add_arc(1, 2, 0)
g.add_arc(2, 2, 0)
self.assertRaises(ValueError, gtn.forward_score, g)
# Throws on cycle
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0)
g.add_arc(1, 2, 0)
g.add_arc(2, 0, 0)
self.assertRaises(ValueError, gtn.forward_score, g)
# Throws if a non-start node has no incoming arcs
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 2, 0)
g.add_arc(1, 2, 0)
self.assertRaises(ValueError, gtn.forward_score, g)
# Handles negative infinity
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, -math.inf)
g.add_arc(0, 1, 1, 1, -math.inf)
self.assertEqual(gtn.forward_score(g).item(), -math.inf)
# Handles infinity
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, math.inf)
g.add_arc(0, 1, 1, 1, 0)
self.assertEqual(gtn.forward_score(g).item(), math.inf)
# Single Node
g = gtn.Graph()
g.add_node(True, True)
self.assertEqual(gtn.forward_score(g).item(), 0.0)
# A simple test case
g = gtn.Graph()
g.add_node(True)
g.add_node()
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 1)
g.add_arc(0, 1, 1, 1, 2)
g.add_arc(0, 1, 2, 2, 3)
g.add_arc(1, 2, 0, 0, 1)
g.add_arc(1, 2, 1, 1, 2)
g.add_arc(1, 2, 2, 2, 3)
self.assertAlmostEqual(gtn.forward_score(g).item(), (6.8152), places=4)
# Handle two start nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, -5)
g.add_arc(0, 2, 0, 0, 1)
g.add_arc(1, 2, 0, 0, 2)
expected = math.log(math.exp(1) + math.exp(-5 + 2) + math.exp(2))
self.assertAlmostEqual(gtn.forward_score(g).item(), (expected), places=4)
# Handle two accept nodes
g = gtn.Graph()
g.add_node(True)
g.add_node(False, True)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 2)
g.add_arc(0, 2, 0, 0, 2)
g.add_arc(1, 2, 0, 0, 2)
expected = math.log(2 * math.exp(2) + math.exp(4))
self.assertAlmostEqual(gtn.forward_score(g).item(), (expected), places=4)
# Handle case where some arcs don't lead to accepting states
g = gtn.Graph()
g.add_node(True)
g.add_node(False, False)
g.add_node(False, True)
g.add_arc(0, 1, 0, 0, 2)
g.add_arc(0, 2, 0, 0, 2)
self.assertEqual(gtn.forward_score(g).item(), 2.0)
# A more complex test case
g_str = [
"0 1",
"3 4",
"0 1 0 0 2",
"0 2 1 1 1",
"1 2 0 0 2",
"2 3 0 0 1",
"2 3 1 1 1",
"1 4 0 0 2",
"2 4 1 1 3",
"3 4 0 0 2",
]
g = create_graph_from_text(g_str)
self.assertAlmostEqual(gtn.forward_score(g).item(), (8.36931), places=4)